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Vector Forms: Lines and Planes

Vector Forms: Lines and Planes
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2017-06-13 11:07
VectorCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates vector representations and visualizations of lines and planes in 3D space. Key math concepts include vectors, dot product, normal vectors, parametric equations of lines, and plane equations. It constructs geometric objects using commands like Vector, Plane, PointIn, Line, Sequence, Point in GeoGebra, showcasing dynamic relationships between lines and planes. Suitable for high school students and learners needing 3D geometry visualization.

GeoGebra Commands & Parameters

  1. Vector(Origin, G) → T1
  2. Plane(A, Origin_B, Origin) → a
  3. PointIn(a) → E
  4. PointIn(a) → Origin_F
  5. Vector(Origin_B, A) → T1_A
  6. Line(qwInitPt, wTermPt) → Line_{2D}
  7. Vector(qwInitPt, wTermPt) → w
  8. Vector(qwInitPt, qwInitPt + (t * w)) → wScl
  9. Vector(O, qwInitPt) → u
  10. Vector(O, qwInitPt + (t * w)) → v
  11. Plane(O, qwInitPt, wTermPt) → n
  12. Vector(qwInitPt, qTermPt) → q
  13. Vector(qwInitPt, qwInitPt + (s * q)) → qScl
  14. Line(qwInitPt, qTermPt) → f_1
  15. Vector(O, qTermPtScl) → v_1
  16. Plane(wTermPt, qwInitPt, qTermPt) → c_1
  17. Sequence(Line[qwInitPt + (t * w), q], t, -15, 15) → qParallelLinesPlane
  18. Sequence(qwInitPt + (t * w), t, -15, 15) → wCoordPts
  19. Sequence(qwInitPt + (s * q), s, -15, 15) → qCoordPts
  20. Sequence(Line[qwInitPt + (s * q), w], s, -15, 15) → wParallelLinesPlane
  21. Sequence(Text[" " + (k), qwInitPt + (k * q)], k, -15, 15) → qAxisNumberList
  22. Vector(wTermPt, wTermPt + Vector[(1, 0, -3)]) → u_1
  23. Vector(wTermPt, wTermPt + Vector[(1, 2, -3)]) → w_1
  24. Vector(wTermPt, wTermPt + Vector[(1, -1, -3)]) → h_1
  25. Point(qwInitPt, Vector[(s * q) + (t * w)]) → GridPt
  26. Sequence(Text[" " + (k), qwInitPt + (k * w)], k, -15, 15) → wAxisNumberList